A fiber-treating agent which improves the water resistance and the heat resistance, imparts heat shape memory ability, and also improves the stretchability and the feel of the surface of a fiber. The fiber-treating agent is a one-part type fiber-treating agent formed of a single composition or a multiple-part type fiber-treating agent formed of a plurality of compositions and comprises the following components (A) to (C) in a total composition: (A): an aromatic compound having one or more vinyl groups or vinylidene groups, and a coordinating functional group; (B): a radical initiator; and (C): water.